V. D. Shafranov and Necessary Conditions for Fusion Energy

Zakharov, L.

doi:10.1134/s1063780x19120092

Cited by 10 publications

(18 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Moreover, some results have shown a crossover * yzhang75@xmu.edu.cn † zhaoh@xmu.edu.cn from the stretched exponential law to a power law for various conditions [15]. Recently, the wave turbulence theory [16][17][18][19][20] was applied to attack this problem [21][22][23]. It was shown analytically and numerically that the exact nontrivial multi-wave resonant interactions were responsible for the thermalization of short FPUT chains in the weakly nonlinear regime and this resulted in T eq following a power law.…”

Section: Introductionmentioning

confidence: 99%

Nonintegrability and thermalization of one-dimensional diatomic lattices

Zhang

Zhao

2019

Phys. Rev. E

View full text Add to dashboard Cite

Nonintegrability is a necessary condition for the thermalization of a generic Hamiltonian system. In practice, the integrability can be broken in various ways. As illustrating examples, we numerically studied the thermalization behaviors of two types of one-dimensional (1D) diatomic chains in the thermodynamic limit. One chain was the diatomic Toda chain whose nonintegrability was introduced by unequal masses. The other chain was the diatomic Fermi-Pasta-Ulam-Tsingou-β chain whose nonintegrability was introduced by quartic nonlinear interaction. We found that these two different methods of destroying the integrability led to qualitatively different routes to thermalization, but the thermalization time, Teq, followed the same law; Teq was inversely proportional to the square of the perturbation strength. This law also agreed with the existing results of 1D monatomic lattices. All these results imply that there is a universal law of thermalization that is independent of the method of breaking integrability.

show abstract

Section: Introductionmentioning

confidence: 99%

Nonintegrability and thermalization of one-dimensional diatomic lattices

Zhang

Zhao

2019

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…The key idea underlying this approach is that, to obtain and retain a high-temperature plasma, it is much easier to prevent thermal conductivity cooling of its boundary by absorbing outgoing particles and blocking the reverse "cold" flow into the plasma than to increase the heating power and deal with growing losses caused by turbulent thermal conductivity in the presence of plasma contact with a cold wall. The productivity of this concept [12] and other possibilities of using lithium requires detailed experimental verification.…”

Section: Tokamak Today: What Is Wrong?mentioning

confidence: 99%

Prospects for Thermonuclear Research

Velikhov

Ilgisonis

2021

Her. Russ. Acad. Sci.

View full text Add to dashboard Cite

Possible prospects for thermonuclear research in the first half of the 21st century and their implementation in the practical sphere of domestic energy are discussed. It is concluded that thermonuclear research can be and already acts as a powerful driver of scientific and technological progress, a mechanism that stimulates the development of high-tech segments of the country's economy, and a possible element of the nuclear energy of the future. This article was prepared based on the materials of a report presented at the General Meeting of RAS Members on December 8, 2020.

show abstract

“…Introducing a cylindrical coordinate system (e r , e φ , e z ) (r = 0 is the major axis of the tokamak torus) and assuming axial symmetry equations (1) and (2) reduce to the following equation for the poloidal flux ψ(r, z) in the poloidal…”

Section: Free-boundary Plasma Equilibriummentioning

confidence: 99%

“…-Ω p is the plasma domain where equations (2) and (1) imply that p and f are constant on each magnetic surface i.e. p = p(ψ) and f = f (ψ).…”

Section: Free-boundary Plasma Equilibriummentioning

confidence: 99%

“…Numerical equilibrium reconstruction is an important and long standing subject in tokamak fusion plasma science [1,2,3,4,5,6]. The resolution of this inverse problem: the reconstruction of the poloidal flux function and of the plasma boundary as well as the identification of two non-linear source term functions known as p and f f in the Grad-Shafranov equation [7,8,9] (see Eq.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimal control of a coupled partial and ordinary differential equations system for the assimilation of polarimetry Stokes vector measurements in tokamak free-boundary equilibrium reconstruction with application to ITER

Faugeras

Blum

Heumann

et al. 2017

Computer Physics Communications

View full text Add to dashboard Cite

International audienceThe modelization of polarimetry Faraday rotation measurements commonly used in tokamak plasma equilibrium reconstruction codes is an approximation to the Stokes model. This approximation is not valid for the foreseen ITER scenarios where high current and electron density plasma regimes are expected. In this work a method enabling the consistent resolution of the inverse equilibrium reconstruction problem in the framework of non-linear free-boundary equilibrium coupled to the Stokes model equation for polarimetry is provided. Using optimal control theory we derive the optimality system for this inverse problem. A sequential quadratic programming (SQP) method is proposed for its numerical resolution. Numerical experiments with noisy synthetic measurements in the ITER tokamak configuration for two test cases, the second of which is an H-mode plasma, show that the method is efficient and that the accuracy of the identification of the unknown profile functions is improved compared to the use of classical Faraday measurements

show abstract

V. D. Shafranov and Necessary Conditions for Fusion Energy

Cited by 10 publications

References 15 publications

Nonintegrability and thermalization of one-dimensional diatomic lattices

Nonintegrability and thermalization of one-dimensional diatomic lattices

Prospects for Thermonuclear Research

Optimal control of a coupled partial and ordinary differential equations system for the assimilation of polarimetry Stokes vector measurements in tokamak free-boundary equilibrium reconstruction with application to ITER

Contact Info

Product

Resources

About